Homework 7

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4) Water has an index of refraction of 1.333, what is the speed of light through it?

n = c/v => v = c/n => v = 3x108 / 1.333 => v = 2.25 x 108 m/s

 

 

6) Two mirrors meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown. (a) Determine the distance the reflected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being reflected from mirror 2?

 

 

 

7) An underwater scuba diver sees the Sun at an apparent angle of 450 from the vertical. What is the actual direction of the Sun with respect to the horizon? The index of refraction of water is 1.333.

n1sinq1 = n2sinq2 => nairsinqi = nwatersinqr => 1sinqi = 1.333 sin45 => sinqi = 0.94257 =>

=> qi = sin-1(0.94257) => qi = 70.5o

φ = 90 - 70.5 = 19.5o above the horizon

 

11) Light has an unknown wavelength λ0 in a vacuum. But the same light has a wavelength of 438 nm in water and a wavelength of 390 nm in benzene. (a) What is the wavelength λ0? The index of refraction of water is 1.333. (b) Using only the given wavelengths, determine the ratio of index of the refraction of benzene to that of water.

n1λ1 = n2λ

 

 

 

 

 

18) A ray of light strikes a flat 2.00-cm-thick block of glass (n= 1.50) at an angle of 300 with the normal. Trace the light beam through the glass, and find the angles of incidence and refraction at each surface.

Snell's law at top interface:

n1sinq1 = n2sinq2 => nairsin30 = nglasssinq => 1x(0.5) = 1.5sinq => sinq = 1/3 =>

=> q = sin-1(1/3) => q = 19.5o  

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Snell's law at bottom interface:

n1sinq1 = n2sinq2 => nglasssin19.5 = nairsinφ => 1.5sin19.5 = 1 sinφ => sinφ = 0.5 =>

=> φ = sin-1(0.5) => φ = 30o  

Hence the exit ray is parallel to the incident ray.

 

 

 

 

19) When the light ray in Problem 18 passes through the glass block, it is shifted laterally by a distance d. Find the value of d.

 

 

 

 

 

24) A narrow beam of ultrasonic waves reflects off a liver tumor (see figure). If the speed of the wave is 10.0 % less in the liver than in the surrounding medium, determine the depth of the tumor.

 

 

 

25) A beam of light both reflects and refracts at the surface between air and glass, as shown in figure. If the index of refraction of the glass is 1.52, find the angle of incidence, Θ1, in the air that would result in the reflected ray and the refracted ray being perpendicular to each other. Use the identity sin(90 - q) = cosq

Requirement: q1 + q2 = 90 => q2 = 90 - q1   

n1sinq1 = n2sinq2 => 1sinq1 = 1.52sinq2 => sinq1 = 1.52sin(90 - q1) =>

=> sinq1 = 1.52cos(q1) => tanq1 = 1.52 => q1 = tan-1(1.52) => q1 = 56.7o

 

 

27) An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the afternoon Sun reaches an angle of 280 above the horizon, sunlight ceases to illuminate the bottom of the tank. How deep is the tank? The index of refraction of water is 1.333.

 

 

 

32) The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 600 if the angle of incidence 500?

 

 

 

37) A plastic light pipe has an index of refraction 1.53. For total internal reflection, what is the minimum angle of incidence if the pipe is in (a) air (the index of refraction of air is 1), (b) water (of index of refraction 1.333)?

 

 

 

38) Determine the maximum angle Θi for which the light rays incident on the end of the light pipe of the figure are subject to total internal reflections along the walls of the pipe. Assume that the light pipe has an index of refraction of 1.36 and that the outside medium is air.